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}), _jsx(_components.span, { className: "vlist-s", children: "​" })] }), _jsx(_components.span, { className: "vlist-r", children: _jsx(_components.span, { className: "vlist", style: { height: "0.15em" }, children: _jsx(_components.span, {}) }) })] }) })] })] })] })] }), _jsx(_components.span, { className: "vlist-s", children: "​" })] }), _jsx(_components.span, { className: "vlist-r", children: _jsx(_components.span, { className: "vlist", style: { height: "1.13em" }, children: _jsx(_components.span, {}) }) })] }) }), _jsx(_components.span, { className: "mclose nulldelimiter" })] })] })] })] }) }) }), "\n", _jsx(_components.p, { children: "式で書くと難しそうに思えるので、実際に計算して文章AとBのcos類似度を求めてみる。" }), "\n", _jsx(_components.p, { children: "文章" }), "\n", _jsx(_components.p, { children: "私" }), "\n", _jsx(_components.p, { children: "リンゴ" }), "\n", _jsx(_components.p, { children: "食べる" }), "\n", _jsx(_components.p, { children: "バナナ" }), "\n", _jsx(_components.p, { children: "買う" }), "\n", _jsx(_components.p, { children: "長さ" }), "\n", _jsx(_components.p, { children: "A. 私はリンゴを食べる。" }), "\n", _jsx(_components.p, { children: "1" }), "\n", _jsx(_components.p, { children: "1" }), "\n", _jsx(_components.p, { children: "1" }), "\n", _jsx(_components.p, { children: "0" }), "\n", _jsx(_components.p, { children: "0" }), "\n", _jsx(_components.p, { children: _jsx(_components.span, { className: "math math-inline", children: _jsxs(_components.span, { className: "katex", children: [_jsx(_components.span, { className: "katex-mathml", children: _jsx(_components.math, { xmlns: "http://www.w3.org/1998/Math/MathML", children: _jsxs(_components.semantics, { children: [_jsx(_components.mrow, { children: _jsx(_components.msqrt, { children: _jsx(_components.mn, { children: "3" }) }) }), _jsx(_components.annotation, { encoding: "application/x-tex", children: "\\sqrt{3}" })] }) }) }), _jsx(_components.span, { className: "katex-html", "aria-hidden": "true", children: _jsxs(_components.span, { 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xmlns: "http://www.w3.org/2000/svg", width: "400em", height: "1.08em", viewBox: "0 0 400000 1080", preserveAspectRatio: "xMinYMin slice", children: _jsx(_components.path, { d: "M95,702\nc-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14\nc0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54\nc44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10\ns173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429\nc69,-144,104.5,-217.7,106.5,-221\nl0 -0\nc5.3,-9.3,12,-14,20,-14\nH400000v40H845.2724\ns-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7\nc-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47z\nM834 80h400000v40h-400000z" }) }) })] })] }), _jsx(_components.span, { className: "vlist-s", children: "​" })] }), _jsx(_components.span, { className: "vlist-r", children: _jsx(_components.span, { className: "vlist", style: { height: "0.1328em" }, children: _jsx(_components.span, {}) }) })] }) })] }) })] }) }) }), "\n", _jsx(_components.p, { children: "B. 私はバナナを食べる。" }), "\n", _jsx(_components.p, { children: "1" }), "\n", _jsx(_components.p, { children: "0" }), "\n", _jsx(_components.p, { children: "1" }), "\n", _jsx(_components.p, { children: "1" }), "\n", _jsx(_components.p, { children: "0" }), "\n", _jsx(_components.p, { children: _jsx(_components.span, { className: "math math-inline", children: _jsxs(_components.span, { className: "katex", children: [_jsx(_components.span, { className: "katex-mathml", children: _jsx(_components.math, { xmlns: "http://www.w3.org/1998/Math/MathML", children: _jsxs(_components.semantics, { children: [_jsx(_components.mrow, { children: _jsx(_components.msqrt, { children: _jsx(_components.mn, { children: "3" }) }) }), _jsx(_components.annotation, { encoding: "application/x-tex", children: "\\sqrt{3}" })] }) }) }), _jsx(_components.span, { className: "katex-html", "aria-hidden": "true", children: _jsxs(_components.span, { className: "base", children: [_jsx(_components.span, { className: 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}), "\n", _jsx(_components.p, { children: "0" }), "\n", _jsx(_components.p, { children: "1" }), "\n", _jsx(_components.p, { children: "0" }), "\n", _jsx(_components.p, { children: "0" }), "\n", _jsx(_components.p, { children: "cos類似度は、文章A×文章Bの和をとって、長さで割ることで算出できる。" }), "\n", _jsx(_components.div, { className: "math math-display", children: _jsx(_components.span, { className: "katex-display", children: _jsxs(_components.span, { className: "katex", children: [_jsx(_components.span, { className: "katex-mathml", children: _jsx(_components.math, { xmlns: "http://www.w3.org/1998/Math/MathML", display: "block", children: _jsxs(_components.semantics, { children: [_jsxs(_components.mrow, { children: [_jsx(_components.mtext, { children: "文章" }), _jsx(_components.mi, { children: "A" }), _jsx(_components.mtext, { children: "と文章" }), _jsx(_components.mi, { children: "B" }), _jsx(_components.mtext, { children: "の" }), _jsx(_components.mi, { children: "c" }), _jsx(_components.mi, { children: "o" }), 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_jsx(_components.annotation, { encoding: "application/x-tex", children: "文章Aと文章Bのcos類似度=\\frac{1+0+1+0+0}{\\sqrt{3} \\times \\sqrt{3}}=\\frac{2}{3}" })] }) }) }), _jsxs(_components.span, { className: "katex-html", "aria-hidden": "true", children: [_jsxs(_components.span, { className: "base", children: [_jsx(_components.span, { className: "strut", style: { height: "0.6833em" } }), _jsx(_components.span, { className: "mord cjk_fallback", children: "文章" }), _jsx(_components.span, { className: "mord mathnormal", children: "A" }), _jsx(_components.span, { className: "mord cjk_fallback", children: "と文章" }), _jsx(_components.span, { className: "mord mathnormal", style: { marginRight: "0.05017em" }, children: "B" }), _jsx(_components.span, { className: "mord cjk_fallback", children: "の" }), _jsx(_components.span, { className: "mord mathnormal", children: "cos" }), _jsx(_components.span, { className: "mord cjk_fallback", children: "類似度" }), _jsx(_components.span, { className: "mspace", style: { 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_jsx(_components.span, { className: "mspace", style: { marginRight: "0.2778em" } })] }), _jsxs(_components.span, { className: "base", children: [_jsx(_components.span, { className: "strut", style: { height: "2.0074em", verticalAlign: "-0.686em" } }), _jsxs(_components.span, { className: "mord", children: [_jsx(_components.span, { className: "mopen nulldelimiter" }), _jsx(_components.span, { className: "mfrac", children: _jsxs(_components.span, { className: "vlist-t vlist-t2", children: [_jsxs(_components.span, { className: "vlist-r", children: [_jsxs(_components.span, { className: "vlist", style: { height: "1.3214em" }, children: [_jsxs(_components.span, { style: { top: "-2.314em" }, children: [_jsx(_components.span, { className: "pstrut", style: { height: "3em" } }), _jsx(_components.span, { className: "mord", children: _jsx(_components.span, { className: "mord", children: "3" }) })] }), _jsxs(_components.span, { style: { top: "-3.23em" }, children: [_jsx(_components.span, { className: "pstrut", style: { height: "3em" } }), _jsx(_components.span, { className: "frac-line", style: { borderBottomWidth: "0.04em" } })] }), _jsxs(_components.span, { style: { top: "-3.677em" }, children: [_jsx(_components.span, { className: "pstrut", style: { height: "3em" } }), _jsx(_components.span, { className: "mord", children: _jsx(_components.span, { className: "mord", children: "2" }) })] })] }), _jsx(_components.span, { className: "vlist-s", children: "​" })] }), _jsx(_components.span, { className: "vlist-r", children: _jsx(_components.span, { className: "vlist", style: { height: "0.686em" }, children: _jsx(_components.span, {}) }) })] }) }), _jsx(_components.span, { className: "mclose nulldelimiter" })] })] })] })] }) }) }), "\n", _jsx(_components.p, { children: "これと同じように、3つの文章のbag-of-wordsからcos類似度を計算してみる。" }), "\n", _jsx(_components.p, { children: "文章1" }), "\n", _jsx(_components.p, { children: "文章2" }), "\n", _jsx(_components.p, { children: "cos類似度" }), "\n", _jsx(_components.p, { children: "私はリンゴを食べる。" }), "\n", _jsx(_components.p, { children: "私はバナナを食べる。" }), "\n", _jsx(_components.p, { children: "0.66" }), "\n", _jsx(_components.p, { children: "私はリンゴを食べる。" }), "\n", _jsx(_components.p, { children: "私はリンゴを買う。" }), "\n", _jsx(_components.p, { children: "0.66" }), "\n", _jsx(_components.p, { children: "私はバナナを食べる。" }), "\n", _jsx(_components.p, { children: "私はリンゴを買う。" }), "\n", _jsx(_components.p, { children: "0.33" }), "\n", _jsx(_components.p, { children: "bag-of-wordsでベクトル化した後のcos類似度は、共起している度合いを計算しているイメージである。共通している単語が多ければ、cos類似度が上がり、似ていると判断される。" }), "\n", _jsx(_components.h3, { children: "Pythonでの実装" }), "\n", _jsxs(_components.p, { children: ["bag-of-wordsでベクトル化さえできていれば、cos類似度の計算は簡単だ。vector_bowは", _jsx(_components.a, { href: "./blog13.html", children: "前回の記事" }), "で作成したものを使用する。"] }), "\n", _jsx(_components.pre, { children: _jsxs(_components.code, { className: "hljs language-python", children: [_jsx(_components.span, { className: "hljs-keyword", children: "import" }), " numpy ", _jsx(_components.span, { className: "hljs-keyword", children: "as" }), " np\n", _jsx(_components.span, { className: "hljs-keyword", children: "def" }), " ", _jsx(_components.span, { className: "hljs-title function_", children: "cos_sim" }), "(", _jsx(_components.span, { className: "hljs-params", children: "v1,v2" }), "):\n ", _jsx(_components.span, { className: "hljs-keyword", children: "return" }), "\n np.dot(v1,v2)/\n np.linalg.norm(v1)/\n np.linalg.norm(v2) v1,v2,v3=vector_bow\n ", _jsx(_components.span, { className: "hljs-built_in", children: "print" }), "(", _jsx(_components.span, { className: "hljs-string", children: "\"v1={},v2={},v3={}\"" }), ".", _jsx(_components.span, { className: "hljs-built_in", children: "format" }), "(v1,v2,v3))\n ", _jsx(_components.span, { className: "hljs-built_in", children: "print" }), "(", _jsx(_components.span, { className: "hljs-string", children: "\"v1とv2のcos類似度:{:.03f}\"" }), ".", _jsx(_components.span, { className: "hljs-built_in", children: "format" }), "(cos_sim(v1,v2)))\n ", _jsx(_components.span, { className: "hljs-built_in", children: "print" }), "(", _jsx(_components.span, { className: "hljs-string", children: "\"v1とv3のcos類似度:{:.03f}\"" }), ".", _jsx(_components.span, { className: "hljs-built_in", children: "format" }), "(cos_sim(v1,v3)))\n ", _jsx(_components.span, { className: "hljs-built_in", children: "print" }), "(", _jsx(_components.span, { className: "hljs-string", children: "\"v2とv3のcos類似度:{:.03f}\"" }), ".", _jsx(_components.span, { className: "hljs-built_in", children: "format" }), "(cos_sim(v2,v3)))\n"] }) }), "\n", _jsx(_components.p, { children: "実行結果" }), "\n", _jsx(_components.pre, { children: _jsx(_components.code, { className: "hljs language-text", children: "v1=[1. 1. 1. 0. 0.],v2=[0. 1. 1. 1. 0.],v3=[1. 1. 0. 0. 1.] v1とv2のcos類似度:0.667 v1とv3のcos類似度:0.667 v2とv3のcos類似度:0.333\n" }) }), "\n", _jsx(_components.h3, { children: "まとめと今後の課題" }), "\n", _jsx(_components.p, { children: "いったんテキストから類似度の算出までを記載した。シンプルではあるが、そこそこ直感と合っていて、理解もしやすい。" }), "\n", _jsx(_components.p, { children: "類似度を算出できれば、次のことができる。" }), "\n", _jsxs(_components.ul, { children: ["\n", _jsx(_components.li, { children: "単語が似た文章の検索" }), "\n", _jsx(_components.li, { children: "文章のクラスタリング" }), "\n"] }), "\n", _jsx(_components.p, { children: "ここら辺はできると思うので、ぜひ試していただきたい。" }), "\n", _jsx(_components.p, { children: "しかし、bag-of-wordsを使用したcos類似度は以下の欠点も存在する。" }), "\n", _jsxs(_components.ul, { children: ["\n", _jsxs(_components.li, { children: ["\n", _jsx(_components.p, { children: "次元数が多いため、計算量が膨大。" }), "\n"] }), "\n", _jsxs(_components.li, { children: ["\n", _jsx(_components.p, { children: "表記揺れで、同じ意味の単語でも別の単語として区別する。(「楽しい」、「たのしい」等)" }), "\n"] }), "\n", _jsxs(_components.li, { children: ["\n", _jsx(_components.p, { children: "別の単語を同じ単語として認識する。(「うまい(美味い、上手い)等」)" }), "\n"] }), "\n", _jsxs(_components.li, { children: ["\n", _jsxs(_components.p, { children: ["文章の並び順を考慮していない。", _jsx(_components.br, {}), "\n", "* 「〜ない」等の否定語の考慮(否定しているのに類似度が高いと出てしまう。)"] }), "\n"] }), "\n"] }), "\n", _jsx(_components.p, { children: "上3つはSVD、LDAなどの次元削減によって解決できる。筆者の余裕があれば今後ブログを書いていく予定。" }), "\n", _jsx(_components.p, { children: "下2つは並び順を考慮しなければならないので、構文解析や、ディープラーニング等をして解決する。こちらもできれば書いていきたい。" })] }); } function MDXContent(props = {}) { const {wrapper: MDXLayout} = Object.assign({}, _provideComponents(), props.components); return MDXLayout ? _jsx(MDXLayout, Object.assign({}, props, { children: _jsx(_createMdxContent, props) })) : _createMdxContent(props); } return { default: MDXContent }; a:["$","div",null,{"className":"container mx-auto px-4 py-8 max-w-7xl","children":["$","div",null,{"className":"flex flex-col md:flex-row gap-8","children":[["$","article",null,{"className":"w-full md:w-[70%] bg-white shadow-lg rounded-lg p-8","children":[["$","header",null,{"className":"mb-8 border-b pb-4","children":[["$","div",null,{"className":"flex items-center gap-2 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